It is wrong to assume that body armor ever became obsolete. Even though you need a relative large amount of armor to protect yourself against bullets close ranged, you need very little to protect yourself against shrapnels. There is more or less no point in time when armor was unable to protect you against on form of battlefield hazard or another. There is sometimes that the military don't use it to gain some form of tactical/strategical advantage.

During the early 1800s the napolonic wars ravaged Europe. During that time periode most armys in Europe would have part of their cavalery using a special type of plate armor called a cuirass. Infantry would normally not be issued any kind of armor. The reason here though is mainly the introduction of mass-drafts. Mass-drafts makes lives cheap, but many countries where having a hard time just getting the most basic equipment (gun, bullets, boots, uniform) to such large amount of troops. Many soldier would instead carry multiple layers of cloth as an improvised gambeson.